A system of variational inequalities arising from finite expiry Russian option with two regimes

In this paper we consider a system of variational inequalities arising from the value of finite expiry Russian option with two regimes. We achieve the existence and uniqueness of the solution to the problem. Moreover, we show that the free boundaries are infinitely differentiable and monotonic with respect to time and some parameters in this system, as well as the mutual relationship between the solutions in two regimes. Moreover, we establish the bound of the free boundaries and analyze their property as time converges to infinite. Copyright © 2009 John Wiley & Sons, Ltd.